To obtain hydrocarbons such as oil and gas, wellbores (also referred to as the boreholes) are drilled by rotating a drill bit attached at the end of a drilling assembly generally referred to as the “bottom hole assembly” (BHA) or the “drilling assembly.” A large portion of the current drilling activity involves drilling highly deviated and substantially horizontal wellbores to increase the hydrocarbon production and/or to withdraw additional hydrocarbons from the earth's formations. The wellbore path of such wells is carefully planned prior to drilling such wellbores utilizing seismic maps of the earth's subsurface and well data from previously drilled wellbores in the associated oil fields. Due to the very high cost of drilling such wellbores and the need to precisely place such wellbores in the reservoirs, it is essential to frequently determine the position and direction of the drilling assembly and thus the drill bit during drilling of the wellbores. Such information is utilized, among other things, to monitor and adjust the drilling direction of the wellbores. It should be noted that the terms “wellbore” and “borehole” are used interchangeably in the present document.
In the commonly used drilling assemblies, the directional package commonly includes a set of accelerometers and a set of magnetometers, which respectively measure the earth's gravity and magnetic fields. The drilling assembly is held stationary during the taking of the measurements from the accelerometers and the magnetometers. The toolface and the inclination angle are determined from the accelerometer measurements. The azimuth is then determined from the magnetometer measurements in conjunction with the tool face and inclination angle. As used herein, the term “toolface” means the orientation angle of the bent housing or sub in the borehole with respect to a reference such as high side of the borehole which indicates the direction in which the borehole will be curving. The inclination angle is the angle between the borehole axis and the vertical (direction of the gravity field). The azimuth is the angle between the horizontal projection of the borehole axis and a reference direction such as magnetic north or absolute north.
The earth's magnetic field varies from day to day, which causes corresponding changes in the magnetic azimuth. The varying magnetic azimuth compromises the accuracy of the position measurements when magnetometers are used. Additionally, it is not feasible to measure the earth's magnetic field in the presence of ferrous or ferromagnetic materials, such as casing and drill pipe. The presence of ferrous or ferromagnetic materials is particularly problematic when kicking-off directly below a casing shoe, or over a whipstock. Gyroscopes measure the rate of the earth's rotation, which does not change with time nor are the gyroscopes adversely affected by the presence of ferrous materials. Thus, in the presence of ferrous materials the gyroscopic measurements can provide more accurate azimuth measurements than the magnetometer measurements. However, gyroscopes have to contend with the large differences in magnitude between the earth rotational rate (approximately 15°/hr) and toolface changes during typical drilling (typically 45°/s). For this reason, it is desirable to determine toolface angles using only accelerometers.